双分销渠道下需求受价格影响的单周期产品供应链订货策略研究

如何协调双分销渠道冲突问题已成为近年来供应链管理领域研究的一个重要议题.本文着重考虑一类制造商生产能力有限且需求受价格影响的双分销渠道供应链订货决策问题.通过数学建模的方式,建立了两类供应链决策模型:(1)以制造商为主方,零售商为从方的Stackelberg主从对策双分销渠道订货决策模型;(2)制造商与零售商合作情形下的双分销渠道集中决策模型,并分别证明了最优的存在性.另外,还利用遗传算法对两类模型进行求解,并通过数值分析得到一些重要的管理启示.  

航空装备战斗损伤概率预测模型研究

装备战场抢修是保持和恢复装备战斗力的重要因素.预测并准确掌握航空装备的损伤概率,有利于作战指挥员和装备保障人员适时而准确的指导战场抢修任务的完成,以保证航空装备的持续作战能力.通过分析航空装备的战伤原因,运用概率分析法构建了航空装备战斗损伤概率预测模型,并提出了模型的改进建议.  

On the spectral radius of ‡-shape trees

Let A(G) be the adjacency matrix of G. The characteristic polynomial of the adjacency matrix A is called the characteristic polynomial of the graph G and is denoted by φ(G, λ) or simply φ(G). The spectrum of G consists of the roots (together with their multiplicities) λ ₁(G) ? λ ₂(G) ? … ? λ _n (G) of the equation φ(G, λ) = 0. The largest root λ ₁(G) is referred to as the spectral radius of G. A ?-shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by G(l ₁, l ₂, … l ₇) (l ₁ ? 0, l _i ? 1, i = 2, 3, …, 7) a ?-shape tree such that $G\left( {l_1 ,l_2 , \ldots l_7 } \right) - u - v = P_{l_1 } \cup P_{l_2 } \cup \ldots P_{l_7 }$ , where u and v are the vertices of degree 4. In this paper we prove that ${{3\sqrt 2 } \mathord{\left/ {\vphantom {{3\sqrt 2 } 2}} \right. \kern-0em} 2} < \lambda _1 \left( {G\left( {l_1 ,l_2 , \ldots l_7 } \right)} \right) < {5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-0em} 2}$ .  

可变抽样区间图经济设计分析

传统控制图是静态的,其抽样区间为固定常数,往往不能及时发现生产过程异常。针对这种情况,本文在综合抽样成本、生产次品损失、误报警和漏报警损失、发现并纠正过程异常成本等基础上,提出可变抽样区间X图的经济设计方法。根据过程实际状态和由抽样结果采取的决策构建了一个二维时间离散的马尔可夫链,提出优化模型,并利用遗传算法寻找控制图参数的最优解。数值计算给出本文模型的具体求解过程。灵敏度分析研究了各参数对最优样本容量、控制限、警戒限、抽样区间及单位时间平均成本的影响。  

On the Laplacian spectral characterization of Π-shape trees

A Π-shape tree is a tree with exactly two vertices having the maximum degree three. In this paper, we classify the Π-shape trees into two types, and complete the spectral characterization for one type. Exactly, we prove that all graphs of this type are determined by their Laplacian spectra with some exceptions. Moreover, we give some L-cospectral mates of some graphs for another type.  

具有五个不同于0和1的Laplacian特征值的单圈图

设$U$是$n$阶单圈图, $m_{U}(1)$是$U$的拉普拉斯特征值1的重数.众所周知,0是连通图重数为1的拉普拉斯特征值.这意味着如果$U$有五个不同于0和1的拉普拉斯特征值,那么$m_U(1)=n-6$.本文完整刻画了$m_U(1)=n-6$的所有单圈图.  

图的剖分点-边冠运算下的规范拉普拉斯谱

A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.  

On the Laplacian integral tricyclic graphs

A graph is called Laplacian integral if all its Laplacian eigenvalues are integers. In this paper, we give an edge subdividing theorem for Laplacian eigenvalues of a graph (Theorem 2.1) and characterize a class of k-cyclic graphs whose algebraic connectivity is less than one. Using these results, we determine all the Laplacian integral tricyclic graphs. Furthermore, we show that all the Laplacian integral tricyclic graphs are determined by their Laplacian spectra.  

带有线性退化和随机振荡的系统可靠性及维修决策

研究了随时间发生线性退化和随机振荡导致瞬时退化的系统可靠度及定期维修策略。随机振荡的发生次数服从非时齐泊松过程,每次振荡造成系统的退化量独立同分布。当累积退化量达到阀值时,系统发生故障。为了改善系统工作状态,降低故障风险,每隔T时对系统进行不完全预防维修,维修后故障率函数将发生变化,维修成本与系统的退化程度有关。在NT时,对系统进行完全预防维修,使系统修旧如新。构建了系统的可靠度函数。在单位时间平均利润最大的前提下,提出不完全预防维修间隔T和完全预防维修周期NT的确定方法。分析了模型参数对维修决策的影响。